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   &#160;<span id="projectnumber">3.4.90 (git rev 67eeba6e720c5745abc77ae6c92ce0a44aa7b7ae)</span>
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<div class="title">MINRES.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2012 Giacomo Po &lt;gpo@ucla.edu&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">// Copyright (C) 2011-2014 Gael Guennebaud &lt;gael.guennebaud@inria.fr&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// Copyright (C) 2018 David Hyde &lt;dabh@stanford.edu&gt;</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160; </div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160; </div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#ifndef EIGEN_MINRES_H</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#define EIGEN_MINRES_H</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160; </div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160; </div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> {</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;    </div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;    <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;        </div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> Rhs, <span class="keyword">typename</span> Dest, <span class="keyword">typename</span> Preconditioner&gt;</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;        EIGEN_DONT_INLINE</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;        <span class="keywordtype">void</span> minres(<span class="keyword">const</span> MatrixType&amp; mat, <span class="keyword">const</span> Rhs&amp; rhs, Dest&amp; x,</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;                    <span class="keyword">const</span> Preconditioner&amp; precond, <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a>&amp; iters,</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;                    <span class="keyword">typename</span> Dest::RealScalar&amp; tol_error)</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;        {</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;            <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;            <span class="keyword">typedef</span> <span class="keyword">typename</span> Dest::RealScalar RealScalar;</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;            <span class="keyword">typedef</span> <span class="keyword">typename</span> Dest::Scalar Scalar;</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;            <span class="keyword">typedef</span> <a class="codeRef" href="../classEigen_1_1Matrix.html">Matrix&lt;Scalar,Dynamic,1&gt;</a> VectorType;</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160; </div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;            <span class="comment">// Check for zero rhs</span></div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;            <span class="keyword">const</span> RealScalar rhsNorm2(rhs.squaredNorm());</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;            <span class="keywordflow">if</span>(rhsNorm2 == 0)</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;            {</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;                x.setZero();</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;                iters = 0;</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;                tol_error = 0;</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;                <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;            }</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;            </div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;            <span class="comment">// initialize</span></div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;            <span class="keyword">const</span> <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> maxIters(iters);  <span class="comment">// initialize maxIters to iters</span></div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;            <span class="keyword">const</span> <a class="codeRef" href="../namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> N(mat.cols());    <span class="comment">// the size of the matrix</span></div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;            <span class="keyword">const</span> RealScalar threshold2(tol_error*tol_error*rhsNorm2); <span class="comment">// convergence threshold (compared to residualNorm2)</span></div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;            </div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;            <span class="comment">// Initialize preconditioned Lanczos</span></div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;            VectorType v_old(N); <span class="comment">// will be initialized inside loop</span></div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;            VectorType v( VectorType::Zero(N) ); <span class="comment">//initialize v</span></div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;            VectorType v_new(rhs-mat*x); <span class="comment">//initialize v_new</span></div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;            RealScalar residualNorm2(v_new.squaredNorm());</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;            VectorType w(N); <span class="comment">// will be initialized inside loop</span></div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;            VectorType w_new(precond.solve(v_new)); <span class="comment">// initialize w_new</span></div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;<span class="comment">//            RealScalar beta; // will be initialized inside loop</span></div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;            RealScalar beta_new2(v_new.dot(w_new));</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;            eigen_assert(beta_new2 &gt;= 0.0 &amp;&amp; <span class="stringliteral">&quot;PRECONDITIONER IS NOT POSITIVE DEFINITE&quot;</span>);</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;            RealScalar beta_new(<a class="codeRef" href="../namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(beta_new2));</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;            <span class="keyword">const</span> RealScalar beta_one(beta_new);</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;            <span class="comment">// Initialize other variables</span></div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;            RealScalar c(1.0); <span class="comment">// the cosine of the Givens rotation</span></div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;            RealScalar c_old(1.0);</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;            RealScalar s(0.0); <span class="comment">// the sine of the Givens rotation</span></div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;            RealScalar s_old(0.0); <span class="comment">// the sine of the Givens rotation</span></div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;            VectorType p_oold(N); <span class="comment">// will be initialized in loop</span></div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;            VectorType p_old(VectorType::Zero(N)); <span class="comment">// initialize p_old=0</span></div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;            VectorType p(p_old); <span class="comment">// initialize p=0</span></div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;            RealScalar eta(1.0);</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;                        </div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;            iters = 0; <span class="comment">// reset iters</span></div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;            <span class="keywordflow">while</span> ( iters &lt; maxIters )</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;            {</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;                <span class="comment">// Preconditioned Lanczos</span></div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;                <span class="comment">/* Note that there are 4 variants on the Lanczos algorithm. These are</span></div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;<span class="comment">                 * described in Paige, C. C. (1972). Computational variants of</span></div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;<span class="comment">                 * the Lanczos method for the eigenproblem. IMA Journal of Applied</span></div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;<span class="comment">                 * Mathematics, 10(3), 373-381. The current implementation corresponds </span></div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;<span class="comment">                 * to the case A(2,7) in the paper. It also corresponds to </span></div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;<span class="comment">                 * algorithm 6.14 in Y. Saad, Iterative Methods for Sparse Linear</span></div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;<span class="comment">                 * Systems, 2003 p.173. For the preconditioned version see </span></div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;<span class="comment">                 * A. Greenbaum, Iterative Methods for Solving Linear Systems, SIAM (1987).</span></div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;<span class="comment">                 */</span></div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;                <span class="keyword">const</span> RealScalar beta(beta_new);</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;                v_old = v; <span class="comment">// update: at first time step, this makes v_old = 0 so value of beta doesn&#39;t matter</span></div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;                v_new /= beta_new; <span class="comment">// overwrite v_new for next iteration</span></div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;                w_new /= beta_new; <span class="comment">// overwrite w_new for next iteration</span></div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;                v = v_new; <span class="comment">// update</span></div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;                w = w_new; <span class="comment">// update</span></div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;                v_new.noalias() = mat*w - beta*v_old; <span class="comment">// compute v_new</span></div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;                <span class="keyword">const</span> RealScalar alpha = v_new.dot(w);</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;                v_new -= alpha*v; <span class="comment">// overwrite v_new</span></div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;                w_new = precond.solve(v_new); <span class="comment">// overwrite w_new</span></div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;                beta_new2 = v_new.dot(w_new); <span class="comment">// compute beta_new</span></div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;                eigen_assert(beta_new2 &gt;= 0.0 &amp;&amp; <span class="stringliteral">&quot;PRECONDITIONER IS NOT POSITIVE DEFINITE&quot;</span>);</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;                beta_new = <a class="codeRef" href="../namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>(beta_new2); <span class="comment">// compute beta_new</span></div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;                </div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;                <span class="comment">// Givens rotation</span></div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;                <span class="keyword">const</span> RealScalar r2 =s*alpha+c*c_old*beta; <span class="comment">// s, s_old, c and c_old are still from previous iteration</span></div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;                <span class="keyword">const</span> RealScalar r3 =s_old*beta; <span class="comment">// s, s_old, c and c_old are still from previous iteration</span></div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;                <span class="keyword">const</span> RealScalar r1_hat=c*alpha-c_old*s*beta;</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;                <span class="keyword">const</span> RealScalar r1 =<a class="codeRef" href="../namespaceEigen.html#af4f536e8ea56702e63088efb3706d1f0">sqrt</a>( std::pow(r1_hat,2) + std::pow(beta_new,2) );</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;                c_old = c; <span class="comment">// store for next iteration</span></div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;                s_old = s; <span class="comment">// store for next iteration</span></div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;                c=r1_hat/r1; <span class="comment">// new cosine</span></div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;                s=beta_new/r1; <span class="comment">// new sine</span></div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;                </div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;                <span class="comment">// Update solution</span></div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;                p_oold = p_old;</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;                p_old = p;</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;                p.noalias()=(w-r2*p_old-r3*p_oold) /r1; <span class="comment">// IS NOALIAS REQUIRED?</span></div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;                x += beta_one*c*eta*p;</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;                </div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;                <span class="comment">/* Update the squared residual. Note that this is the estimated residual.</span></div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;<span class="comment">                The real residual |Ax-b|^2 may be slightly larger */</span></div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;                residualNorm2 *= s*s;</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;                </div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;                <span class="keywordflow">if</span> ( residualNorm2 &lt; threshold2)</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;                {</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;                    <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;                }</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;                </div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;                eta=-s*eta; <span class="comment">// update eta</span></div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;                iters++; <span class="comment">// increment iteration number (for output purposes)</span></div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;            }</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;            </div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;            <span class="comment">/* Compute error. Note that this is the estimated error. The real </span></div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;<span class="comment">             error |Ax-b|/|b| may be slightly larger */</span></div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;            tol_error = std::sqrt(residualNorm2 / rhsNorm2);</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;        }</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;        </div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;    }</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;    </div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;    <span class="keyword">template</span>&lt; <span class="keyword">typename</span> MatrixType_, <span class="keywordtype">int</span> UpLo_=<a class="codeRef" href="../group__enums.html#gga39e3366ff5554d731e7dc8bb642f83cdaf581029282d421eee5aae14238c6f749">Lower</a>,</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;    <span class="keyword">typename</span> Preconditioner_ = IdentityPreconditioner&gt;</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;    <span class="keyword">class </span>MINRES;</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;    </div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;    <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;        </div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;        <span class="keyword">template</span>&lt; <span class="keyword">typename</span> MatrixType_, <span class="keywordtype">int</span> UpLo_, <span class="keyword">typename</span> Preconditioner_&gt;</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;        <span class="keyword">struct </span>traits&lt;MINRES&lt;MatrixType_,UpLo_,Preconditioner_&gt; &gt;</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;        {</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;            <span class="keyword">typedef</span> MatrixType_ MatrixType;</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;            <span class="keyword">typedef</span> Preconditioner_ Preconditioner;</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;        };</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;        </div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;    }</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;    </div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;    <span class="keyword">template</span>&lt; <span class="keyword">typename</span> MatrixType_, <span class="keywordtype">int</span> UpLo_, <span class="keyword">typename</span> Preconditioner_&gt;</div>
<div class="line"><a name="l00197"></a><span class="lineno"><a class="line" href="classEigen_1_1MINRES.html">  197</a></span>&#160;    <span class="keyword">class </span><a class="code" href="classEigen_1_1MINRES.html">MINRES</a> : <span class="keyword">public</span> <a class="codeRef" href="../classEigen_1_1IterativeSolverBase.html">IterativeSolverBase</a>&lt;MINRES&lt;MatrixType_,UpLo_,Preconditioner_&gt; &gt;</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;    {</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;        </div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;        <span class="keyword">typedef</span> <a class="codeRef" href="../classEigen_1_1IterativeSolverBase.html">IterativeSolverBase&lt;MINRES&gt;</a> <a class="codeRef" href="../classEigen_1_1IterativeSolverBase.html">Base</a>;</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;        <span class="keyword">using</span> Base::matrix;</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;        <span class="keyword">using</span> Base::m_error;</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;        <span class="keyword">using</span> Base::m_iterations;</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;        <span class="keyword">using</span> Base::m_info;</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;        <span class="keyword">using</span> Base::m_isInitialized;</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;    <span class="keyword">public</span>:</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;        <span class="keyword">using</span> Base::_solve_impl;</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;        <span class="keyword">typedef</span> MatrixType_ MatrixType;</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;        <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;        <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;        <span class="keyword">typedef</span> Preconditioner_ Preconditioner;</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;        </div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;        <span class="keyword">enum</span> {UpLo = UpLo_};</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;        </div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;    <span class="keyword">public</span>:</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;        </div>
<div class="line"><a name="l00218"></a><span class="lineno"><a class="line" href="classEigen_1_1MINRES.html#a11841032b43f03d27dd2817c944428f5">  218</a></span>&#160;        <a class="code" href="classEigen_1_1MINRES.html#a11841032b43f03d27dd2817c944428f5">MINRES</a>() : <a class="codeRef" href="../classEigen_1_1IterativeSolverBase.html">Base</a>() {}</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;        </div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixDerived&gt;</div>
<div class="line"><a name="l00231"></a><span class="lineno"><a class="line" href="classEigen_1_1MINRES.html#a772d4c93859e7b26ab974820e37beddd">  231</a></span>&#160;        <span class="keyword">explicit</span> <a class="code" href="classEigen_1_1MINRES.html#a772d4c93859e7b26ab974820e37beddd">MINRES</a>(<span class="keyword">const</span> <a class="codeRef" href="../structEigen_1_1EigenBase.html">EigenBase&lt;MatrixDerived&gt;</a>&amp; A) : <a class="codeRef" href="../classEigen_1_1IterativeSolverBase.html">Base</a>(A.derived()) {}</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;        </div>
<div class="line"><a name="l00234"></a><span class="lineno"><a class="line" href="classEigen_1_1MINRES.html#aae1a169d6dd1cd81f769c6bae0f450be">  234</a></span>&#160;        <a class="code" href="classEigen_1_1MINRES.html#aae1a169d6dd1cd81f769c6bae0f450be">~MINRES</a>(){}</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160; </div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;        <span class="keyword">template</span>&lt;<span class="keyword">typename</span> Rhs,<span class="keyword">typename</span> Dest&gt;</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;        <span class="keywordtype">void</span> _solve_vector_with_guess_impl(<span class="keyword">const</span> Rhs&amp; b, Dest&amp; x)<span class="keyword"> const</span></div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;<span class="keyword">        </span>{</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;            <span class="keyword">typedef</span> <span class="keyword">typename</span> Base::MatrixWrapper <a class="codeRef" href="../classEigen_1_1MatrixWrapper.html">MatrixWrapper</a>;</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;            <span class="keyword">typedef</span> <span class="keyword">typename</span> Base::ActualMatrixType ActualMatrixType;</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;            <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;              TransposeInput  =   (!MatrixWrapper::MatrixFree)</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;                              &amp;&amp;  (UpLo==(<a class="codeRef" href="../group__enums.html#gga39e3366ff5554d731e7dc8bb642f83cdaf581029282d421eee5aae14238c6f749">Lower</a>|<a class="codeRef" href="../group__enums.html#gga39e3366ff5554d731e7dc8bb642f83cdafca2ccebb604f171656deb53e8c083c1">Upper</a>))</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;                              &amp;&amp;  (!MatrixType::IsRowMajor)</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;                              &amp;&amp;  (!<a class="codeRef" href="../structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::IsComplex</a>)</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;            };</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;            <span class="keyword">typedef</span> std::conditional_t&lt;TransposeInput,Transpose&lt;const ActualMatrixType&gt;, ActualMatrixType <span class="keyword">const</span>&amp;&gt; RowMajorWrapper;</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;            EIGEN_STATIC_ASSERT(internal::check_implication(MatrixWrapper::MatrixFree, UpLo==(<a class="codeRef" href="../group__enums.html#gga39e3366ff5554d731e7dc8bb642f83cdaf581029282d421eee5aae14238c6f749">Lower</a>|<a class="codeRef" href="../group__enums.html#gga39e3366ff5554d731e7dc8bb642f83cdafca2ccebb604f171656deb53e8c083c1">Upper</a>)),MATRIX_FREE_CONJUGATE_GRADIENT_IS_COMPATIBLE_WITH_UPPER_UNION_LOWER_MODE_ONLY);</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;            <span class="keyword">typedef</span> std::conditional_t&lt;UpLo==(<a class="codeRef" href="../group__enums.html#gga39e3366ff5554d731e7dc8bb642f83cdaf581029282d421eee5aae14238c6f749">Lower</a>|<a class="codeRef" href="../group__enums.html#gga39e3366ff5554d731e7dc8bb642f83cdafca2ccebb604f171656deb53e8c083c1">Upper</a>),</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;                                                  RowMajorWrapper,</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;                                                  <span class="keyword">typename</span> MatrixWrapper::template ConstSelfAdjointViewReturnType&lt;UpLo&gt;::Type</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;                                            &gt; SelfAdjointWrapper;</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160; </div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;            m_iterations = <a class="codeRef" href="../classEigen_1_1IterativeSolverBase.html#a168a74c8dceb6233b220031fdd756ba0">Base::maxIterations</a>();</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;            m_error = Base::m_tolerance;</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;            RowMajorWrapper row_mat(matrix());</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;            internal::minres(SelfAdjointWrapper(row_mat), b, x,</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;                             Base::m_preconditioner, m_iterations, m_error);</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;            m_info = m_error &lt;= Base::m_tolerance ? <a class="codeRef" href="../group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Success</a> : <a class="codeRef" href="../group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea6a68dfb88a8336108a30588bdf356c57">NoConvergence</a>;</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;        }</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;        </div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;    <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;        </div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;    };</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160; </div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160; </div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_MINRES_H</span></div>
<div class="ttc" id="aclassEigen_1_1IterativeSolverBase_html"><div class="ttname"><a href="../classEigen_1_1IterativeSolverBase.html">Eigen::IterativeSolverBase</a></div></div>
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<div class="ttc" id="aclassEigen_1_1MINRES_html"><div class="ttname"><a href="classEigen_1_1MINRES.html">Eigen::MINRES</a></div><div class="ttdoc">A minimal residual solver for sparse symmetric problems.</div><div class="ttdef"><b>Definition:</b> MINRES.h:198</div></div>
<div class="ttc" id="aclassEigen_1_1MINRES_html_a11841032b43f03d27dd2817c944428f5"><div class="ttname"><a href="classEigen_1_1MINRES.html#a11841032b43f03d27dd2817c944428f5">Eigen::MINRES::MINRES</a></div><div class="ttdeci">MINRES()</div><div class="ttdef"><b>Definition:</b> MINRES.h:218</div></div>
<div class="ttc" id="aclassEigen_1_1MINRES_html_a772d4c93859e7b26ab974820e37beddd"><div class="ttname"><a href="classEigen_1_1MINRES.html#a772d4c93859e7b26ab974820e37beddd">Eigen::MINRES::MINRES</a></div><div class="ttdeci">MINRES(const EigenBase&lt; MatrixDerived &gt; &amp;A)</div><div class="ttdef"><b>Definition:</b> MINRES.h:231</div></div>
<div class="ttc" id="aclassEigen_1_1MINRES_html_aae1a169d6dd1cd81f769c6bae0f450be"><div class="ttname"><a href="classEigen_1_1MINRES.html#aae1a169d6dd1cd81f769c6bae0f450be">Eigen::MINRES::~MINRES</a></div><div class="ttdeci">~MINRES()</div><div class="ttdef"><b>Definition:</b> MINRES.h:234</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixWrapper_html"><div class="ttname"><a href="../classEigen_1_1MatrixWrapper.html">Eigen::MatrixWrapper</a></div></div>
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<div class="ttc" id="agroup__enums_html_gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf"><div class="ttname"><a href="../group__enums.html#gga85fad7b87587764e5cf6b513a9e0ee5ea671a2aeb0f527802806a441d58a80fcf">Eigen::Success</a></div><div class="ttdeci">Success</div></div>
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<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div></div>
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